Constellation rearrangement for transmit diversity schemes

ABSTRACT

A method of transmitting data in a wireless communication system from a transmitter to a receiver, comprising the steps of modulating data at the transmitter using a first signal constellation pattern to obtain a first data symbol. The first data symbol is transmitted to the receiver using a first diversity branch. Further, the data is modulated at the transmitter using a second signal constellation pattern to obtain a second data symbol. Then, the second data symbol is transmitted to the receiver over a second diversity path. Finally, the received first and second data symbol are diversity combined at the receiver. 
     The invention further relates to a transmitter and a receiver embodied to carry out the method of the invention.

This is a continuation application of application Ser. No. 11/634,127filed Dec. 6, 2006 (pending), which is a continuation of applicationSer. No. 10/501,905 filed Jul. 20, 2004, which issued as U.S. Pat. No.7,164,727 on Jan. 16, 2007, which is a national phase application of PCTinternational application number PCT/EP2002/011695 filed on Oct. 18,2002, the entire contents of each of which are incorporated by referenceherein.

The present invention relates generally to transmission techniques inwireless communication systems and in particular to a method,transceiver and receiver using transmit diversity schemes wherein thebit-to-symbol mapping is performed differently for different transmitteddiversity branches. The invention is particularly applicable to systemswith unreliable and time-varying channel conditions resulting in animproved performance avoiding transmission errors.

There exist several well known transmit diversity techniques wherein oneor several redundancy versions relating to identical data aretransmitted on several (at least two) diversity branches “by default”without explicitly requesting (by a feedback channel) further diversitybranches (as done in an ARQ scheme by requesting retransmissions). Forexample the following schemes are considered as transmit diversity:

-   -   Site Diversity: The transmitted signal originates from different        sites, e.g. different base stations in a cellular environment.    -   Antenna Diversity: The transmitted signal originates from        different antennas, e.g. different antennas of a multi-antenna        base station.    -   Polarization Diversity: The transmitted signal is mapped onto        different polarizations.    -   Frequency Diversity: The transmitted signal is mapped e.g. on        different carrier frequencies or on different frequency hopping        sequences.    -   Time Diversity: The transmitted signal is e.g. mapped on        different interleaving sequences.    -   Multicode Diversity: The transmitted signal is mapped on        different codes in e.g. a CDMA (Code Division Multiple Access)        system.

There are known several diversity combining techniques. The followingthree techniques are the most common ones:

-   -   Selection Combining: Selecting the diversity branch with the        highest SNR for decoding, ignoring the remaining ones.    -   Equal Gain Combining: Combining received diversity branches with        ignoring the differences in received SNR.    -   Maximal Ratio Combining: Combining received diversity branches        taking the received SNR of each diversity branch into account.        The combining can be performed at bit-level (e.g. LLR) or at        modulation symbol level.

Furthermore, a common technique for error detection/correction is basedon Automatic Repeat reQuest (ARQ) schemes together with Forward ErrorCorrection (FEC), called hybrid ARQ (HARQ). If an error is detectedwithin a packet by the Cyclic Redundancy Check (CRC), the receiverrequests the transmitter to send additional information (retransmission)to improve the probability to correctly decode the erroneous packet.

In WO-02/067491 A1 a method for hybrid ARQ transmissions has beendisclosed which averages the bit reliabilities over successivelyrequested retransmissions by means of signal constellationrearrangement.

As shown therein, when employing higher order modulation formats (e.g.M-PSK, M-QAM with log₂(M)>2), where more than 2 bits are mapped onto onemodulation symbol, the bits mapped onto a modulation symbol havedifferent reliabilities depending on their content and depending on thechosen mapping. This leads for most FEC (e.g. Turbo Codes) schemes to adegraded decoder performance compared to an input of more equallydistributed bit reliabilities.

In conventional communication systems the modulation dependentvariations in bit reliabilities are not taken into account and, hence,usually the variations remain after combining the diversity branches atthe receiver.

The object of the invention is to provide a method, transmitter andreceiver which show an improved performance with regard to transmissionerrors. This object is solved by a method, transmitter and receiver asset forth in the independent claims.

The invention is based on the idea to improve the decoding performanceat the receiver by applying different signal constellation mappings tothe available distinguishable transmit diversity branches. The idea isapplicable to modulation formats, where more than 2 bits are mapped ontoone modulation symbol, since this implies a variation in reliabilitiesfor the bits mapped onto the signal constellation (e.g. for regular BPSKand QPSK modulation all bits mapped onto a modulation symbol have thesame reliability). The variations depend on the employed mapping and onthe actually transmitted content of the bits.

Depending on the employed modulation format and the actual number ofbits mapped onto a single modulation symbol, for a given arbitrarynumber (N>1) of available diversity branches the quality of theaveraging process is different. Averaging in the sense of the presentinvention is understood as a process of reducing the differences in meancombined bit reliabilities among the different bits of a data symbol.Although it might be that only after using several diversity branches orpaths a perfect averaging with no remaining differences is achieved,averaging means in the context of the document any process steps in thedirection of reducing the mean combined bit reliability differences.Assuming on average an equal SNR for all available diversity branches,for 16-QAM 4 mappings (4 diversity branches) would be needed toperfectly average out the reliabilities for all bits mapped on anysymbol. However, if e.g. only 2 branches are available a perfectaveraging is not possible. Hence, the averaging should then be performedon a best effort basis as shown in the example below.

The present invention will be more readily understood from the followingdetailed description of preferred embodiments with reference to theaccompanying figures which show:

FIG. 1 an example for a 16-QAM signal constellation;

FIG. 2 an example for a different mapping of a 16-QAM signalconstellation;

FIG. 3 two further examples of 16-QAM signal constellations;

FIG. 4 an exemplary embodiment of a communication system according tothe present invention; and

FIG. 5 details of a table for storing a plurality of signalconstellation patterns.

The following detailed description is shown for a square 16-QAM withGray mapping. However, without loss of generality the shown example isextendable to other M-QAM and M-PSK (with log₂(M)>2) formats. Moreover,the examples are shown for transmit diversity schemes transmitting anidentical bit-sequence on both branches (single redundancy versionscheme). Then again, an extension to a transmit diversity schemetransmitting only partly identical bits on the diversity branches can beaccomplished. An example for a system using multiple redundancy versionsis described in copending EP 01127244, filed on Nov. 16, 2001. Assuminga turbo encoder, the systematic bits can be averaged on a higher levelas compared to the parity bits.

Assuming a transmit diversity scheme with two generated diversitybranches, which are distinguishable at the receiver (e.g. by differentspreading or scrambling codes in a CDMA system, or other techniques ofcreating orthogonal branches) and a transmission of the same redundancyversion, usually the received diversity branches are combined at thereceiver before applying the FEC decoder. A common combining techniqueis the maximal ratio combining, which can be achieved by adding thecalculated log-likelihood-ratios LLRs from each individual receiveddiversity branch.

The log-likelihood-ratio LLR as a soft-metric for the reliability of ademodulated bit b from a received modulation symbol r=x+jy is defined asfollows:

$\begin{matrix}{{{LLR}(b)} = {\ln \left\lbrack \frac{\Pr \left\{ {b = {1\left. r \right\}}} \right.}{\Pr \left\{ {b = {0\left. r \right\}}} \right.} \right\rbrack}} & (1)\end{matrix}$

As can be seen from FIG. 1 (bars indicate rows/columns for which therespective bit equals 1), the mappings of the in-phase component bitsand the quadrature component bits on the signal constellation areorthogonal (for M-PSK the LLR calculation cannot be simplified byseparating into complex components, however the general procedure ofbit-reliability averaging is similar). Therefore, it is sufficient tofocus on the in-phase component bits i₁ and i₂. The same conclusionsapply then for q₁ and q₂.

Assuming that Mapping 1 from FIG. 1 is applied for the bit-to-symbolmapping for the 1^(st) diversity branch, the log-likelihood-ratio LLR ofthe most significant bit (MSB) i₁ and the least significant bit (LSB) i₂yields the following equations for a Gaussian channel:

$\begin{matrix}{{{LLR}\left( i_{1} \right)} = {\ln \left\lbrack \frac{^{- {K{({x + x_{0}})}}^{2}} + ^{- {K{({x + x_{1}})}}^{2}}}{^{- {K{({x - x_{0}})}}^{2}} + ^{- {K{({x - x_{1}})}}^{2}}} \right\rbrack}} & (2) \\{{{LLR}\left( i_{2} \right)} = {\ln \left\lbrack \frac{^{- {K{({x - x_{1}})}}^{2}} + ^{- {K{({x + x_{1}})}}^{2}}}{^{- {K{({x - x_{0}})}}^{2}} + ^{- {K{({x + x_{0}})}}^{2}}} \right\rbrack}} & (3)\end{matrix}$

where x denotes the in-phase component of the normalized receivedmodulation symbol r and K is a factor proportional to thesignal-to-noise ratio. Under the assumption of a uniform signalconstellation (x₁=3 x_(0,) regular 16-QAM) equations (2) and (3) can befairly good approximated as shown in S. Le Goff, A. Glavieux, C. Berrou,“Turbo-Codes and High Spectral Efficiency Modulation,” IEEESUPERCOMM/ICC '94, Vol. 2 , pp. 645-649, 1994, and Ch. Wengerter, A.Golitschek Edler von Elbwart, E. Seidel, G. Velev, M. P. Schmitt,“Advanced Hybrid ARQ Technique Employing a Signal ConstellationRearrangement,” IEEE Proceedings of VTC 2002 Fall, Vancouver, Canada,September 2002 by

LLR(i ₁)≈−4Kx ₀ x  (4)

LLR(i ₂)≈−4Kx ₀(2x ₀ −|x|)  (5)

The mean LLR for i₁ and i₂ for a given transmitted modulation symbolyields the values given in Table 1 (substituting 4Kx₀ ² by Λ). Mean inthis sense, refers to that the mean received value for a giventransmitted constellation point, exactly matches this transmittedconstellation point. Individual samples of course experience noiseaccording to the parameter K. However, for a Gaussian channel the meanvalue of the noise process is zero. In case of transmitted modulationsymbols 0q₁1q₂ and 1q₁1q₂, where q₁ and q₂ are arbitrary, the magnitudeof the mean LLR(i₁) is higher than of the mean LLR (i₂). This means thatthe LLR for the MSB i₁ depends on the content of the LSB i₂; e.g. inFIG. 1 i₁ has a higher mean reliability in case the logical value for i₂equals 1 (leftmost and rightmost columns). Hence, assuming a uniformdistribution of transmitted modulation symbols, on average 50% of theMSBs i₁ have about three times the magnitude in LLR of i₂.

TABLE 1 Mean LLRs for bits mapped on the in-phase component of thesignal constellation for Mapping 1 in FIG. 1 according to equations (4)and (5). Symbol Mean value (i₁q₁i₂q₂) of x Mean LLR (i₁) Mean LLR (i₂)0q₁0q₂ x₀ −4Kx₀ ² = −Λ −4Kx₀ ² = −Λ 0q₁1q₂ x₁ −12Kx₀ ² = −3Λ 4Kx₀ ² = Λ1q₁0q₂ −x₀  4Kx₀ ² = Λ −4Kx₀ ² = −Λ 1q₁1q₂ −x₁  12Kx₀ ² = 3Λ 4Kx₀ ² = Λ

If now adding a 2^(nd) transmit diversity branch transmitting e.g. anidentical bit sequence prior art schemes would employ an identicalmapping to the 1^(st) diversity branch. Here, it is proposed to employ a2^(nd) signal constellation mapping (Mapping 2) according to FIG. 2 (ofcourse, also one of the constellations depicted in FIG. 3 are possible),which yields the mean LLRs given in Table 2.

TABLE 2 Mean LLRs for bits mapped on the in-phase component of thesignal constellation for Mapping 2 in FIG. 2. Symbol Mean value(i₁q₁i₂q₂) of x Mean LLR (i₁) Mean LLR (i₂) 0q₁0q₂ x₀ −Λ  −3Λ  0q₁1q₂ x₁−Λ  3Λ 1q₁0q₂ −x₀  Λ −Λ 1q₁1q₂ −x₁  Λ  Λ

Comparing now the soft-combined LLRs of the received diversity branchesapplying the constellation rearrangement (Mapping 1+2) and applying theidentical mappings (Mapping 1+1, prior art), it can be observed fromtable 3 that the combined mean LLR values with applying theconstellation rearrangement have a more uniform distribution(Magnitudes: 4×4 Λ and 4×2 Λ instead of 2×6 Λ and 6×2 Λ). For most FECdecoders (e.g. Turbo Codes and Convolutional Codes) this leads to abetter decoding performance. Investigations have revealed that inparticular Turbo encoding/decoding systems exhibit a superiorperformance. It should be noted, that the chosen mappings are nonexhaustive and more combinations of mappings fulfilling the samerequirements can be found.

TABLE 3 Mean LLRs (per branch) and combined mean LLRs for bits mapped onthe in-phase component of the signal constellation for the diversitybranches when employing Mapping 1 and 2 and when employing 2 timesMapping 1. Constellation Prior Art Rearrangement No RearrangementTransmit (Mapping 1 + 2) (Mapping 1 + 1) Diversity Symbol Mean Mean MeanMean Branch (i₁q₁i₂q₂) LLR (i₁) LLR (i₂) LLR (i₁) LLR (i₂) 1 0q₁0q₂ −Λ−Λ −Λ −Λ 0q₁1q₂ −3Λ Λ −3Λ Λ 1q₁0q₂ Λ −Λ Λ −Λ 1q₁1q₂ 3Λ Λ 3Λ Λ 2 0q₁0q₂−Λ −3Λ −Λ −Λ 0q₁1q₂ −Λ 3Λ −3Λ Λ 1q₁0q₂ Λ −Λ Λ −Λ 1q₁1q₂ Λ Λ 3Λ ΛCombined 0q₁0q₂ −2Λ −4Λ −2Λ −2Λ 1 + 2 0q₁1q₂ −4Λ −4Λ −6Λ 2Λ 1q₁0q₂ 2Λ−2Λ 2Λ −2Λ 1q₁1q₂ 4Λ 2Λ 6Λ 2Λ

In the following an example with 4 diversity branches will be described.Here, the same principles apply as for 2 diversity branches. However,since 4 diversity branches are available and the averaging with 2diversity branches is not perfect, additional mappings can be used toimprove the averaging process.

FIG. 3 shows the additional mappings for diversity branches 3 and 4,under the assumption that Mappings 1 and 2 are used for branches 1 and 2(in FIG. 1 and FIG. 2). Then the averaging can be performed perfectlyand all bits mapped on any symbol will have an equal mean bitreliability (assuming the same SNR for all transmissions). Table 4compares the LLRs with and without applying the proposed ConstellationRearrangement. Having a closer look at the combined LLRs, it can be seenthat with application of the Constellation Rearrangement the magnitudefor all bit reliabilities results in 6 Λ.

It should be noted again, that the chosen mappings are non exhaustiveand more combinations of mappings fulfilling the same requirements canbe found.

TABLE 4 Mean LLRs (per branch) and combined mean LLRs for bits mapped onthe in-phase component of the signal constellation for the diversitybranches when employing Mappings 1 to 4 and when employing 4 timesMapping 1. Constellation Prior Art Rearrangement No Rearrangement(Mapping 1 + (Mapping 1 + Transmit 2 + 3 + 4) 1 + 1 + 1) DiversitySymbol Mean Mean Mean Mean Branch (i₁q₁i₂q₂) LLR (i₁) LLR (i₂) LLR (i₁)LLR (i₂) 1 0q₁0q₂ −Λ −Λ −Λ −Λ 0q₁1q₂ −3Λ Λ −3Λ Λ 1q₁0q₂ Λ −Λ Λ −Λ 1q₁1q₂3Λ Λ 3Λ Λ 2 0q₁0q₂ −Λ −3Λ −Λ −Λ 0q₁1q₂ −Λ 3Λ −3Λ Λ 1q₁0q₂ Λ −Λ Λ −Λ1q₁1q₂ Λ Λ 3Λ Λ 3 0q₁0q₂ −Λ −Λ −Λ −Λ 0q₁1q₂ −Λ Λ −3Λ Λ 1q₁0q₂ Λ −3Λ Λ −Λ1q₁1q₂ Λ 3Λ 3Λ Λ 4 0q₁0q₂ −3Λ −Λ −Λ −Λ 0q₁1q₂ −Λ Λ −3Λ Λ 1q₁0q₂ 3Λ −Λ Λ−Λ 1q₁1q₂ Λ Λ 3Λ Λ Combined 0q₁0q₂ −6Λ −6Λ −4Λ −4Λ 1 + 2 + 0q₁1q₂ −6Λ 6Λ−12Λ 4Λ 3 + 4 1q₁0q₂ 6Λ −6Λ 4Λ −4Λ 1q₁1q₂ 6Λ 6Λ 12Λ 4Λ

If the constellation rearrangement is performed by applying differentmapping schemes, one would end up in employing a number of differentmappings as given in FIG. 1, FIG. 2 and FIG. 3. If the identical mapper(e.g. FIG. 1) should be kept for all transmit diversity branches, e.g.mapping 2 can be obtained from mapping 1 by the following operations.

-   -   exchange positions of original bits i₁ and i₂    -   exchange positions of original bits q₁ and q₂    -   logical bit inversion of original bits i₁ and q₁

Alternatively, those bits that end in positions 1 and 2 can also beinverted (resulting in a different mapping with an identicalbit-reliability characteristics).

Therefore, the following table provides an example how to obtainmappings 1 to 4 (or mappings with equivalent bit reliabilities for i₁,i₂, q₁ and q₂), where the bits always refer to the first transmission,and a long dash above a character denotes logical bit inversion of thatbit:

TABLE 5 Alternative implementation of the Constellation Rearrangement byinterleaving (intra-symbol interleaving) and logical inversion of bitsmapped onto the modulation symbols. Interleaver and Inverter Mapping No.functionality 1 i₁q₁i₂q₂ 2 ī₂ q ₂ī₁ q ₁ or ī₂ q ₂ī₁ q ₁ 3 ī₂ q ₂ī₁ q ₁or ī₂ q ₂ī₁ q ₁ 4 ī₁ q ₁ī₂ q ₂ or ī₁ q ₁ī₂ q ₂

Generally at least 2 different mappings should be employed for N>1diversity branches, where the order and the selection of the mappings isirrelevant, as long as the bit-reliability averaging process, meaningthe (reduction of differences in reliabilities) is maintained.

Preferred realizations in terms of number of employed mappings

-   -   M-QAM        -   Employing log₂(M) different mappings        -   Employing log₂(M)/2 different mappings    -   M-PSK        -   Employing log₂(M) different mappings        -   Employing log₂(M)/2 different mappings        -   Employing 2 log₂(M) different mappings

The applied signal constellation mappings for modulation at thetransmitter and demodulation at the receiver need to match for eachindividual transmit diversity branch. This can be achieved byappropriate signalling of parameters indicating the proper mapping orcombination of mappings to be applied for the diversity branches.Alternatively the definition of the mappings to be applied for transmitdiversity branches may be system predefined.

FIG. 4 shows an exemplary embodiment of a communication system accordingto the present invention. More specifically, the communication systemcomprises a transmitter 10 and a receiver 20 which communicate through acommunication channel consisting of a plurality of diversity branches40A, 40B and 40C. Although three diversity branches are illustrated inthe figure, it becomes clear to a person skilled in the art that anarbitrary number of branches may be chosen. From a data source 11, datapackets are supplied to a FEC encoder 12, preferably a FEC Turboencoder, where redundancy bits are added to correct errors. The bitsoutput from the FEC encoder are subsequently supplied to a mapping unit13 acting as a modulator to output symbols formed according to theapplied modulation scheme stored as a constellation pattern in a table15. Subsequently the data symbols are applied to a transmission unit 30for transmission over the branches 40A-C. The receiver 20 receives thedata packets by the receiving unit 35. The bits are then input into ademapping unit 21 which acts as a demodulator using the same signalconstellation pattern stored in the table 15 which was used during themodulation of that symbol.

The demodulated data packets received over one diversity branch arestored in a temporary buffer 22 for subsequent combining in a combiningunit 23 with the data packets received over at least one other diversitybranch.

As illustrated in FIG. 5, table 15 stores a plurality of signalconstellation patterns #0 . . . #n which are selected for the individualtransmissions over the individual diversity branches according to apredetermined scheme. The scheme, i.e. the sequence of signalconstellation patterns used for modulating/demodulating are eitherpre-stored in the transmitter and the receiver or are signalled bytransmitter to the receiver prior to usage.

1. A method of transmitting data in a wireless communication system, themethod comprising: modulating and mapping data using a first signalconstellation pattern to obtain a first data symbol; modulating andmapping said data using a second signal constellation pattern which isdifferent from the first signal constellation pattern to obtain a seconddata symbol; and transmitting the first data symbol and the second datasymbol to a receiver.
 2. The method according to claim 1, wherein eachof the first data symbol and the second data symbol is obtained bymapping more than two data bits into one data symbol.
 3. The methodaccording to claim 1, wherein each of the first data symbol and thesecond data symbol is obtained by mapping four data bits into one datasymbol using a 16-QAM modulation scheme.
 4. The method according toclaim 1, wherein the first and second signal constellation patterns areobtained by: (a) interleaving the positions of the bits mapped into onedata symbol between the first and second signal constellation patterns,or (b) inverting the bit values of the bits mapped into one data symbolbetween the first and second signal constellation patterns.
 5. Themethod according to claim 2, wherein the first and second signalconstellation patterns are obtained by: (a) interleaving the positionsof the bits mapped into one data symbol between the first and secondsignal constellation patterns, or (b) inverting the bit values of thebits mapped into one data symbol between the first and second signalconstellation patterns.
 6. The method according to claim 3, wherein thefirst and second signal constellation patterns are obtained by: (a)interleaving the positions of the bits mapped into one data symbolbetween the first and second signal constellation patterns, or (b)inverting the bit values of the bits mapped into one data symbol betweenthe first and second signal constellation patterns.
 7. The methodaccording to claim 1, wherein the first and second signal constellationpatterns are selected such that after diversity combining the data bits,the differences in bit reliabilities among the different bitarrangements of one data symbol are reduced.
 8. The method according toclaim 4, wherein the first and second signal constellation patterns areselected such that after diversity combining the data bits, thedifferences in bit reliabilities among the different bit arrangements ofone data symbol are reduced.
 9. A transmitter for transmitting data in awireless communication system, the transmitter comprising: a firstmodulation and mapping section that modulates and maps data using afirst signal constellation pattern to obtain a first data symbol; asecond modulation and mapping section that modulates and maps said datausing a second signal constellation pattern which is different from thefirst signal constellation pattern to obtain a second data symbol, and atransmission section that transmits the first data symbol and the seconddata symbol to a receiver.
 10. The transmitter according to claim 9,wherein the first and second modulation and mapping sectionsrespectively obtain the first data symbol and the second data symbol bymapping more than two data bits into one data symbol.
 11. Thetransmitter according to claim 9, wherein the first and secondmodulation and mapping sections respectively obtain the first datasymbol and the second data symbol by mapping four data bits into onedata symbol using a 16-QAM modulation scheme.
 12. The transmitteraccording to claim 9, wherein the first and second signal constellationpatterns by one of: (a) interleaving the positions of the bits mappedinto one data symbol between the first and second signal constellationpatterns, and (b) inverting the bit values of the bits mapped into onedata symbol between the first and second signal constellation patterns.13. The transmitter according to claim 10, wherein the first and secondsignal constellation patterns are obtained by one of: (a) interleavingthe positions of the bits mapped into one data symbol between the firstand second signal constellation patterns, and (b) inverting the bitvalues of the bits mapped into one data symbol between the first andsecond signal constellation patterns.
 14. The transmitter according toclaim 11, wherein the first and second signal constellation patterns areobtained by one of: (a) interleaving the positions of the bits mappedinto one data symbol between the first and second signal constellationpatterns, and (b) inverting the bit values of the bits mapped into onedata symbol between the first and second signal constellation patterns.15. The transmitter according to claim 9, wherein the first and secondsignal constellation patterns are selected such that after diversitycombining the data bits, the differences in bit reliabilities among thedifferent bit arrangements of one data symbol are reduced.
 16. Thetransmitter according to claim 12, wherein the first and second signalconstellation patterns are selected such that after diversity combiningthe data bits, the differences in bit reliabilities among the differentbit arrangements of one data symbol are reduced.